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Discrete diffusion has achieved state-of-the-art performance, outperforming or approaching autoregressive models on standard benchmarks. In this work, we introduce Discrete Diffusion with Planned Denoising (DDPD), a novel framework that separates the generation process into two models: a planner and a denoiser. At inference time, the planner selects which positions to denoise next by identifying the most corrupted positions in need of denoising, including both initially corrupted and those requiring additional refinement. This plan-and-denoise approach enables more efficient reconstruction during generation by iteratively identifying and denoising corruptions in the optimal order. DDPD outperforms traditional denoiser-only mask diffusion methods, achieving superior results on language modeling benchmarks such as text8, OpenWebText, and token-based image generation on ImageNet 256×256. Notably, in language modeling, DDPD significantly reduces the performance gap between diffusion-based and autoregressive methods in terms of generative perplexity. 

Discrete diffusion has achieved state-of-the-art performance, outperforming or approaching autoregressive models on standard benchmarks. In this work, we introduce Discrete Diffusion with Planned Denoising (DDPD), a novel framework that separates the generation process into two models: a planner and a denoiser. At inference time, the planner selects which positions to denoise next by identifying the most corrupted positions in need of denoising, including both initially corrupted and those requiring additional refinement. This plan-and-denoise approach enables more efficient reconstruction during generation by iteratively identifying and denoising corruptions in the optimal order. DDPD outperforms traditional denoiser-only mask diffusion methods, achieving superior results on language modeling benchmarks such as text8, OpenWebText, and token-based image generation on ImageNet 256×256. Notably, in language modeling, DDPD significantly reduces the performance gap between diffusion-based and autoregressive methods in terms of generative perplexity. 

Abstract We extend the free convolution of Brown measures of $$R$$-diagonal elements introduced by Kösters and Tikhomirov [ 28] to fractional powers. We then show how this fractional free convolution arises naturally when studying the roots of random polynomials with independent coefficients under repeated differentiation. When the proportion of derivatives to the degree approaches one, we establish central limit theorem-type behavior and discuss stable distributions. 

Abstract Lasso peptides are an increasingly relevant class of peptide natural products with diverse biological activities, intriguing physical properties, and unique chemical structures. Most characterized lasso peptides have been from Actinobacteria and Proteobacteria, despite bioinformatic analyses suggesting that other bacterial taxa, particularly those from Firmicutes, are rich in biosynthetic gene clusters (BGCs) encoding lasso peptides. Herein, we report the bioinformatic identification of a lasso peptide BGC fromPaenibacillus taiwanensisDSM18679 which we termedpats. We used a bioinformatics‐guided isolation approach and high‐resolution tandem mass spectrometry (HRMS/MS) to isolate and subsequently characterize a new lasso peptide produced from thepatsBGC, which we named trilenodin, after the tri‐isoleucine motif present in its primary sequence. This tri‐isoleucine motif is unique among currently characterized lasso peptides. We confirmed the connection between thepatsBGC and trilenodin production by establishing the firstBacillus subtilis168‐based heterologous expression system for expressing Firmicutes lasso peptides. We finally determined that trilenodin exhibits potent antimicrobial activity againstB. subtilisandKlebsiella pneumoniae, making trilenodin the first characterized biologically active lasso peptide from Firmicutes. Collectively, we demonstrate that bacteria from Firmicutes can serve as high‐potential sources of chemically and biologically diverse lasso peptides. 

Using first-principles calculations, this study evaluates the structure, equation of state, and elasticity of three compositions of phase D up to 75 GPa: (1) the magnesium endmember [MgSi2O4(OH)2], (2) the aluminum endmember [Al2SiO4(OH)2], and (3) phase D with 50% Al-substitution [AlMg0.5Si1.5O4(OH)2]. We find that the Mg-endmember undergoes hydrogen-bond symmetrization and that this symmetrization is linked to a 22% increase in the bulk modulus of phase D, in agreement with previous studies. Al2SiO4(OH)2 also undergoes hydrogen-bond symmetrization, but the concomitant increase in bulk modulus is only 13%—a significant departure from the 22% increase of the Mg-endmember. Additionally, Al-endmember phase D is denser (2%–6%), less compressible (6%–25%), and has faster compressional (6%–12%) and shear velocities (12%–15%) relative to its Mg-endmember counterpart. Finally, we investigated the properties of phase D with 50% Al-substitution [AlMg0.5Si1.5O4(OH)2], and found that the hydrogen-bond symmetrization, equation of state parameters, and elastic constants of this tie-line composition cannot be accurately modeled by interpolating the properties of the Mg- and Al-endmembers.